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2022 Microlocal partition of energy for linear wave or Schrödinger equations
Jean-Marc Delort
Tunisian J. Math. 4(2): 329-385 (2022). DOI: 10.2140/tunis.2022.4.329

Abstract

We prove a microlocal partition of energy for solutions to linear half-wave or Schrödinger equations in any space dimension. This extends well-known (local) results valid for the wave equation outside the wave cone, and allows us in particular, in the case of even dimension, to generalize the radial estimates due to Côte, Kenig and Schlag to nonradial initial data.

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Jean-Marc Delort. "Microlocal partition of energy for linear wave or Schrödinger equations." Tunisian J. Math. 4 (2) 329 - 385, 2022. https://doi.org/10.2140/tunis.2022.4.329

Information

Received: 25 May 2021; Accepted: 6 January 2022; Published: 2022
First available in Project Euclid: 2 September 2022

Digital Object Identifier: 10.2140/tunis.2022.4.329

Subjects:
Primary: 35L05
Secondary: 35Q41

Keywords: channels of energy , microlocal analysis , Schrödinger equation , wave equation

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2022
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